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Let p,q and r be the distinct roots of the polynomial x^3 −22x^2 +80x−67. There exist real number A,B and C such that (1/(s^3 −22s^2 +80s−67)) = (A/(s−p)) + (B/(s−q)) + (C/(s−r)) for all real numbers s with s ∉ {p,q,r}.What is (1/A) + (1/B) + (1/C) ? (a) 243 (b) 244 (c) 245 (d)246 (e) 247

$L e t p, q a n d r b e t h e d i s t i n c t r o o t s$ $o f t h e p o l y n o m i a l x^{3} - 22 x^{2} + 80 x - 67 .$ $T h e r e e x i s t r e a l n u m b e r A, B a n d$ $C s u c h t h a t \frac{1}{s^{3} - 22 s^{2} + 80 s - 67} =$ $\frac{A}{s - p} + \frac{B}{s - q} + \frac{C}{s - r} f o r a l l r e a l n u m b e r s$ $s w i t h s \notin {p, q, r} . W h a t i s$ $\frac{1}{A} + \frac{1}{B} + \frac{1}{C} ?$ $(a) 243 (b) 244 (c) 245 (d) 246$ $(e) 247$

Question Number 135557 Answers: 1 Comments: 0

(1/(1−cos θ−i sin θ)) =? i=(√(−1))

$\frac{1}{1 - \cos θ - i \sin θ} = ?$ $i = \sqrt{- 1}$

Question Number 134960 Answers: 1 Comments: 0

Number theory A palindrome is a number that reads the same backwards as forwards, as 3141413. (a)How many two-digit palindromes are there? (b)How many three-digit ones? (c)How many k-digits ones?

$Number theory$ A palindrome is a number that reads the same backwards as forwards, as 3141413. (a)How many two-digit palindromes are there? (b)How many three-digit ones? (c)How many k-digits ones?

Question Number 134458 Answers: 0 Comments: 0

Find the last two digits of 2025^(2052) + 1392^(1329) ?

$Find the last two digits of$ $2025^{2052} + 1392^{1329} ?$

Question Number 134393 Answers: 0 Comments: 0

Σ_(k=0) ^∞ ((4^k (k!)^2 )/((2k+1)^2 (2k)!)) =?

$\underset{k = 0}{\sum^{\infty}} \frac{4^{k} {(k!)}^{2}}{{(2 k + 1)}^{2} (2 k)!} = ?$

Question Number 134327 Answers: 1 Comments: 0

Question Number 134267 Answers: 1 Comments: 0

{ ((x≡ 4 (mod 5))),((x≡ 3 (mod 4 ))) :}

${\begin{cases} x \equiv 4 (\mod 5) \\ x \equiv 3 (\mod 4) \end{cases}$

Question Number 134252 Answers: 1 Comments: 0

solve { ((x≡ 2 (mod 3))),((x≡ 5 (mod 7))) :}

$solve {\begin{cases} x \equiv 2 (\mod 3) \\ x \equiv 5 (\mod 7) \end{cases}$

Question Number 134208 Answers: 0 Comments: 0

Determine if the series Σ_(n=1) ^∞ a_n by the formula converges or diverges . a_1 = 7, a_(n+1) = ((9n+3sin n)/(4n+5cos n)).a_n (a) converges (b) diverges

$Determine if the series \underset{n = 1}{\sum^{\infty}} a_{n}$ $by the formula converges or$ $diverges . a_{1} = 7, a_{n + 1} = \frac{9 n + 3 \sin n}{4 n + 5 \cos n} . a_{n}$ $(a) converges$ $(b) diverges$

Question Number 134069 Answers: 1 Comments: 2

Given a,b and c are real numbers and a<b<c. If (1/a) + (1/b) + (1/c) = (1/(18)) , find minimum value of a.

$G i v e n a, b a n d c a r e r e a l n u m b e r s a n d a < b < c .$ $I f \frac{1}{a} + \frac{1}{b} + \frac{1}{c} = \frac{1}{18}, f i n d m i n i m u m v a l u e o f a .$

Question Number 134037 Answers: 1 Comments: 0

Question Number 133897 Answers: 2 Comments: 0

Find the least positive integer that leaves a remainder 3 when divided by 7 , 4 when divided by 9 , and 8 when divided by 11.

$Find the least positive integer$ $that leaves a remainder 3 when divided by 7$ $, 4 when divided by 9, and 8 when$ $divided by 11 .$

Question Number 133761 Answers: 1 Comments: 0

Solve the linear congruence 19x ≡ 4 (mod 141 )

$Solve the linear congruence$ $19 x \equiv 4 (\mod 141)$

Pg 3 Pg 4 Pg 5 Pg 6 Pg 7 Pg 8 Pg 9 Pg 10 Pg 11 Pg 12

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